Gudder’s Theorem and the Born Rule
We derive the Born probability rule from Gudder’s theorem—a theorem that addresses orthogonally-additive functions. These functions are shown to be tightly connected to the functions that enter the definition of a signed measure. By imposing some additional requirements besides orthogonal additivity...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/3/158 |
| _version_ | 1818036128198950912 |
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| author | Francisco De Zela |
| author_facet | Francisco De Zela |
| author_sort | Francisco De Zela |
| collection | DOAJ |
| description | We derive the Born probability rule from Gudder’s theorem—a theorem that addresses orthogonally-additive functions. These functions are shown to be tightly connected to the functions that enter the definition of a signed measure. By imposing some additional requirements besides orthogonal additivity, the addressed functions are proved to be linear, so they can be given in terms of an inner product. By further restricting them to act on projectors, Gudder’s functions are proved to act as probability measures obeying Born’s rule. The procedure does not invoke any property that fully lies within the quantum framework, so Born’s rule is shown to apply within both the classical and the quantum domains. |
| first_indexed | 2024-12-10T07:06:01Z |
| format | Article |
| id | doaj.art-5633298f330d4f63af1282096d02a2fc |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T07:06:01Z |
| publishDate | 2018-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5633298f330d4f63af1282096d02a2fc2022-12-22T01:58:11ZengMDPI AGEntropy1099-43002018-03-0120315810.3390/e20030158e20030158Gudder’s Theorem and the Born RuleFrancisco De Zela0Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, PeruWe derive the Born probability rule from Gudder’s theorem—a theorem that addresses orthogonally-additive functions. These functions are shown to be tightly connected to the functions that enter the definition of a signed measure. By imposing some additional requirements besides orthogonal additivity, the addressed functions are proved to be linear, so they can be given in terms of an inner product. By further restricting them to act on projectors, Gudder’s functions are proved to act as probability measures obeying Born’s rule. The procedure does not invoke any property that fully lies within the quantum framework, so Born’s rule is shown to apply within both the classical and the quantum domains.http://www.mdpi.com/1099-4300/20/3/158Born probability rulequantum-classical relationshipspinors in quantum and classical physics |
| spellingShingle | Francisco De Zela Gudder’s Theorem and the Born Rule Entropy Born probability rule quantum-classical relationship spinors in quantum and classical physics |
| title | Gudder’s Theorem and the Born Rule |
| title_full | Gudder’s Theorem and the Born Rule |
| title_fullStr | Gudder’s Theorem and the Born Rule |
| title_full_unstemmed | Gudder’s Theorem and the Born Rule |
| title_short | Gudder’s Theorem and the Born Rule |
| title_sort | gudder s theorem and the born rule |
| topic | Born probability rule quantum-classical relationship spinors in quantum and classical physics |
| url | http://www.mdpi.com/1099-4300/20/3/158 |
| work_keys_str_mv | AT franciscodezela gudderstheoremandthebornrule |